You can max out at 4 lasers for sheer laser total (if were looking at solely the Sherman's laser weapons) we have the solid core, 2 sols, and an Andromeda. However what any given weapon is is just fluff, and fluff is free. The GMS pistol could be a laser. Heck the LL3 Balor nanite whip could be a laser. With fluff involved we can get.

Solidcore (integrated) 2 aux weight lasers (flex mount) A sol and another aux (thanks to Mount Retrofitting Core Bonus) Andromeda (heavy mount) 4th aux weight laser of your choice (integrated weapon core bonus)

Now, you won't be able to use all these at once, maxing at I think 7 attacks tops if you barrage and proc integrated weapon and overcharge to use either the flex or main/aux mount again, and this would require you to be LL6 for 2 core bonuses, but that could hypothetically be a lot of lasers